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Chapter 5—Using Newton’s Laws: Friction, Circular Motion, Drag Forces Application of Newton’s Laws Involving Friction   

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Friction exists between 2 solid surfaces, no matter how smooth Rolling friction—when a round object rolls across a surface Kinetic friction—sliding friction o The force of friction opposes motion (opposite direction of objects velocity) o The magnitude of the force depends on the nature of the 2 sliding surfaces  Friction has a magnitude proportional to the normal force o Ffr = µk FN  The magnitude of friction force is parallel to the 2 surfaces  The magnitude of normal force is perpendicular to the 2 surfaces  µk is roughly independent of the sliding speed and the area in contact Static Friction o A force parallel to the 2 surfaces that arises even without sliding  Push a desk without it moving means there is static friction o It is easier to keep a heavy object sliding that to start it sliding because µ s is > µk o Ffr ≤ µs FN Friction as a hindrance o Slows down moving objects & causes heating and binding of moving parts of machinery o Reduce friction between 2 surfaces by maintaining a layer of air or gas between them Example o A box against a wall  The horizontal force applied = normal force and cancel out  The mg down equals the friction force upwards Acceleration = ∑F / m o ∑F = ma

Uniform Circular Motion—Kinematics 

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If the net force acts at an angle to the direction of motion at any moment, then the object moves in a curved path o Uniform circular motion—an object that moves in a circle at constant speed v  The magnitude remains constant, but the direction changes Acceleration o Centripetal/radial acceleration—center pointing o ∆v = (v/r)∆l o aR = v2/r o An object moving in a circle of radius r at a constant speed v has an acceleration whose direction is toward the center of the circle and whose magnitude is aR = v2/r Acceleration points inwards and velocity points in the direction of motion, tangential to the curve o The two vectors are perpendicular to each other Circular motion described in frequency and Time

T = 1/f For an object revolving in a circle (circumference of 2πr) at constant speed  V = 2πr / T Centrifugation o The macromolecule would tend to follow the dashed line heading toward the bottom of the tube, but the fluid forces resist this motion by exerting a force on the particle inward o o

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Dynamics of Uniform Circular Motion  

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∑FR = maR = m(v2/r) For uniform circular motion (v is constant), the acceleration is aR, which is directed toward the center of the circle at any moment o The net force too must be directed toward the center of the circle  The net force is necessary to keep object moving in a circle (0 net F means moving in a straight line) o Centripetal force merely describes the direction of the net force, which is applied by other objects There is no outward force on a revolving object (both forces are inward) o There is a force no the hand exerted by the string o A force on the ball exerted by the string

Highway Curves: Banked and Unbanked 

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